Translation and rotation positioning motor

ABSTRACT

A positioning device provides the capability of moving an object in both a linear and a rotational direction. The positioning device includes a first piezo stack with plural piezo plates that are capable of movement in orthogonal directions with respect to each other. The positioning device further includes a second piezo stack with plural piezo plates that are capable of movement in orthogonal directions with respect to each other. The positioning device also includes a first bearing that is disposed against the first piezo stack. The positioning device further includes a second bearing that is disposed against the second piezo stack. The positioning device also includes a spring element and a fifth bearing that is disposed against the spring element. The first through fifth bearings are disposed around and against the object to be positioned, to provide for positioning of the object in at least one of a linear direction and a rotational direction.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a translation and rotation positioning motor,which can be used for providing precise linear and rotational movementsof a scanning tunneling microscope, for example. In particular, theinvention relates to a translation and rotation positioning motor thatincludes piezo actuators and that provides for movement of an object byangstrom level or sub-angstrom level increments on one or more planes,and that is capable of repeated precise realignment of the object sothat it can be moved repeatedly to a desired position.

2. Description of the Related Art

Scanning tunneling microscopes (STM) are widely used in industry and inresearch to obtain atomic-scale images of specimen surfaces. An STMprovides a three-dimensional profile of the surface, which is useful forcharacterizing surface roughness, observing surface defects, anddetermining surface structure with atomic resolution. An STM operates byproviding a needle point of the STM in very close proximity to thespecimen surface to be scanned, whereby the needle point is moved aboutthe surface in a raster-like manner. The needle point is disposed at adistance from the specimen surface so that a tunneling effect isachieved, whereby, when a voltage is provided to the needle point,electrons “tunnel” from the needle point to the specimen surface. Bymoving the needle point with respect to an opposite point on thespecimen surface in order to obtain a particular current flow, a plot ofthe specimen surface characteristic at that point is obtained. Byrastering the needle point about different parts of the specimensurface, a three dimensional plot of the specimen surface is obtained.

In order to bring the needle point of the STM close enough (but not incontact) to the specimen surface to achieve the desired tunnelingeffect, the needle point is moved by way of a coarse positioning deviceof the STM. Once in the “tunneling region”, a fine positioning device ofthe STM is utilized in order to obtain a precise positioning of theneedle point with respect to the specimen surface to be scanned.

One such positioning device that allows for microscopic movements of ascanning tunneling microscope, and that can be used as either a coarseadjusting device or as a fine adjusting device for an STM, is describedin U.S. Pat. No. 5,237,238, issued to Thomas Berghaus et al., which isincorporated in its entirety herein by reference. The Berghaus et al.patent describes various types of positioning devices, some of whichallow for both linear and rotational movement of an element. FIGS. 15and 15 a of the Berghaus et al. patent show a first adjusting devicethat allows for both linear and rotary movement of a turntable.Referring now to FIG. 15 d of the Berghaus et al. patent, rotarymovement of a turntable 5 is accomplished by way of drive elements 6 aand 6 b, each of which includes a bearing element. Linear movement ofthe turntable 5 is accomplished by way of drive element 6 c, which isfitted within a groove 34 on the bottom surface of the turntable 5.

FIG. 17 of the Berghaus et al. patent shows a second adjusting devicethat allows for both linear and rotary movement. Rotary movement of aturntable 5 is accomplished by way of a rotary adjusting device 1, whilelinear movement of the turntable 5 is accomplished by way of a linearadjusting device 1′ (which has a bearing element of triangularcross-section).

Another conventional microscopic adjusting device is described inpublished European Patent Application WO 93/19494, by Shuheng Pan, whichis incorporated in its entirety herein by reference. The Pan apparatusprovides for microscopic movement of an object in a step-by-step manner,whereby piezo actuators (elements 2 a-2 d as shown in FIG. 1 a of Pan)are moved individually (or in groups) in one direction successivelywhile the remaining actuators hold the object still, and when all of theactuators have been moved, they are simultaneously moved in the oppositedirection. The simultaneous movement of the actuators in the oppositedirection results in linear movement of the object. Differentembodiments described by Pan include an embodiment shown in FIG. 5 ofPan, which allows for rotational movement of a sphere 50 about a centerpoint of the sphere.

None of the conventional microscopic adjusting devices described aboveallows for x-y-z movement of an object using a single adjusting devicethat provides the capability of movement of the object in both a lineardirection and a rotational direction.

Also, the geometrical structure of objects being moved in theapparatuses of Berghaus and Pan are not believed by the inventors ofthis application to be ideal for allowing rotational and linear movementof an object.

SUMMARY OF THE INVENTION

The present invention is directed to an apparatus for moving an objectby way of piezo actuators. According to one aspect of the invention, theapparatus includes a first piezo stack which has a first piezo-electricplate and a second piezo-electric plate that are disposed against eachother and that are capable of movement in orthogonal directions withrespect to each other. The apparatus also includes a second piezo stackwhich has a third piezo-electric plate and a fourth piezo-electric platethat are disposed against each other and that are capable of movement inorthogonal directions with respect to each other. The apparatus furtherincludes a first bearing that is disposed against the first piezo stack,and a second bearing that is disposed against the second piezo stack.The apparatus still further includes a third piezo stack which has afifth piezo-electric plate and a sixth piezo-electric plate that aredisposed against each other and that are capable of movement inorthogonal directions with respect to each other. The apparatus alsoincludes a fourth piezo stack which has a seventh piezo-electric plateand an eighth piezo-electric plate that are disposed against each otherand that are capable of movement in orthogonal directions with respectto each other. The apparatus further includes a third bearing that isdisposed against the third piezo stack, and a fourth bearing that isdisposed against the fourth piezo stack. The apparatus further includesa fifth bearing that is disposed against a spring element. The firstthrough fifth bearings are disposed around and against a cylindricalobject to be moved in at least one of a linear direction and arotational direction.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing advantages and features of the invention will becomeapparent upon reference to the following detailed description and theaccompanying drawings, of which:

FIG. 1 shows a top view of a positioning device according to anembodiment of the invention;

FIG. 2 a shows an unactuated piezo-electric element that may be used inthe positioning device according to an embodiment of the invention;

FIG. 2 b shows an actuated piezo-electric element that may be used inthe positioning device according to an embodiment of the invention;

FIG. 3 shows a voltage waveform that may be used to provide movements ofthe piezo-electric elements used in the positioning device according anembodiment of the invention; and

FIG. 4 shows a plan view of a biaxial piezo actuator that may beutilized in an embodiment of the invention;

FIG. 5 shows a plan view of a cylindrical object that may be positionedin accordance with an embodiment of the invention;

FIG. 6 shows a plan view of biaxial piezo actuators provided on acylindrical object, in accordance with an embodiment of the invention;and

FIG. 7 shows a plan view of a three-dimensional sample stressing andscanning device, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Preferred embodiments of the invention will be described in detailbelow, with reference to the accompanying drawings.

The present invention will be described below with reference to a coarsepositioning device for an STM, but one of ordinary skill in the art willrecognize that the present invention may be utilized for other types ofpositioning devices, such as for a fine positioning device for an STM, astrain motor for straining an object, or for a positioning device for anapparatus to be precisely stepped in units of angstroms and/orsub-angstroms to a particular location.

A coarse positioning device of an STM typically moves the needle tip ofthe STM in units of microns or millimeters, whereby a fine positioningdevice of the STM typically moves the needle tip of the STM insub-micron units.

The adjusting device according to the present invention functions as amotor, and provides for multi-dimensional positioning of objects withsub-micrometer precision. The motor utilizes shear piezo-electricceramics to drive the motion of a cylinder linearly along the axis ofthe cylinder, and also to provide for rotation of the cylinder, asdesired. The cylinder may be used as a strain motor for straining anobject to be scanned, for example, or it may be used as part of a coarseor fine adjusting element of an STM that is used to scan an object.

FIG. 1 shows a top view of a motor 150 according to a first embodimentof the present invention. The motor 150 operates to move a cylinder 160,which is preferably a sapphire cylinder. Sapphire is chosen since theouter surface of the cylinder 160 is preferably very smooth, to allowfor positioning the cylinder 160 in precise, small amounts by way ofbearings that slide on the outer surface of the cylinder 160. One ofordinary skill in the art will recognize that other materials for thecylinder 160 may be contemplated, such as tungsten carbide or polishedsteel, whereby those other materials provide for a hard and very smoothouter surface of the cylinder 160, and whereby the outer surface of thecylinder 160 is not damaged (e.g., not scratched) by bearings slidingthereon. The inventors have found that the material construction of thecylinder 160 should be harder than the material construction of thebearings supporting the cylinder 160, so that the bearings do not damagethe outer surface of the cylinder as they slide on the outer surface.

With regards to the object to be adjusted, the first embodiment of thepresent invention is used to position a cylindrical object, which isdifferent from the prism-shaped object structure of Pan (see FIG. 2A ofPan) or the hexagonal-shaped object structure of Berghaus et al. (seeFIG. 6 of Berghaus et al.)+each of which has flat surfaces. By using acylinder (which has no flat surfaces on an outer circumferential surfacethereof) as the object to be positioned in the first embodiment, thefirst embodiment of the present invention allows for both rotational andlinear movement of the cylinder by way of a plurality of bearingsdisposed around and against the outer circumferential surface of thecylinder.

In particular, due to the configuration of the object to be positionedin the present invention having a cylindrical shape, smooth rotationalmovement to any amount of rotation (e.g., 360 degrees rotation) andsmooth linear translational movement to any amount of translation ispossible. This is a feature that is not possible when the object to bepositioned is a prism (as in Pan) or a hexagon (as in Berghaus et al.),which both prevent rotation.

In an STM configuration, a needle tip or probe (not shown) is fittedonto one end of the cylinder 160. The needle tip or probe is used toobtain a plot of the surface of a specimen (e.g., top surface of afabricated semiconductor device) to be scanned by the STM, as describedpreviously.

In the first embodiment, by way of example and not by way of limitation,the sapphire cylinder 160 is {fraction (1/2)} inch in diameter and 1inch in length. Of course, other sizes of cylinders may be contemplatedwhile remaining within the scope of the invention. The cylinder 160 isheld in place within the motor 150 by five bearings 165A-165E (onlybearings 165A, 165C and 165E are shown in the top view of FIG. 1, sincebearings 165B and 165D are blocked from view), whereby the bearings165A-165D are preferably alumina bearings, and whereby the bearing 165Eis preferably a Teflon bearing. Other constructions for the bearings165A-165D may be contemplated, such as aluminum metal, or tungstencarbide, which allow for smooth sliding of the bearings on the outercircumferential surface of the cylinder 160. Though not shown in FIG. 1,bearings 165B and 165D are positioned beneath the bearings 165A and165C, respectively, in the same manner as piezo actuators 80B and 80Dare positioned with respect to piezo actuators 80A and 80C in the planview of FIG. 6, which shows a different embodiment.

Each of the bearings 165A-165D is mounted on a piezo stack that includestwo piezo plates 180, whereby each one of the bearings 165A-165D iscapable of moving independently of the other three bearings. In thefirst embodiment, the bearings 165A-165D are either half-balls orhalf-cylinders, which are glued directly to the respective top piezoplates. Other ways of fixedly adhering the bearings 165A-165D to the toppiezo plate besides gluing may be contemplated while remaining withinthe scope of the invention. If half-cylinders are used for the bearings,the axis of the half-cylinders should be oriented at 90 degrees withrespect to the cylinder 160.

FIG. 4 shows a biaxial piezo actuator 80A, Which includes ahalf-cylinder bearing 165A′ instead of a half-ball bearing. FIG. 4 alsoshows the two axes by which the bearing 165A′ can move due to theshearing of one or both of the two piezo plates that are part of thebiaxial piezo actuator 80A.

The bearings 165A-165D are configured to slide on the outer surface ofthe cylinder 160. In the first embodiment, the fifth bearing 165E isalso preferably a half-ball or a half-cylinder, which is affixed (e.g.,glued) to a leaf spring.

Referring back to FIG. 1, the fifth bearing 165E is fixed (e.g., glued)to a spring 190, which is preferably a stainless steel leaf spring. Thespring 190 provides a sufficient pressure to the cylinder 160 by way ofthe fifth bearing 165E, to thereby hold the cylinder 160 in place withrespect to the first through fourth bearings 165A-165D that are also incontact with an outer circumferential surface of the cylinder 160. Byway of example and not by way of limitation, the amount of pressureexerted on the cylinder 160 by the combination of the leaf spring 190and the fifth bearing 165E is 1 to 2 Newtons.

The bearing 165E is preferably a Teflon-coated bearing in the firstembodiment, whereby it acts as a slippery bearing and provides lessfriction force than any of the other bearings to the outercircumferential surface of the cylinder 160. Other types ofconstructions may be envisioned to provide for a slippery bearing as thefifth bearing 165E, such as polished alumina or tungsten carbide, whileremaining within the scope of the invention.

The purpose of the combination of the leaf spring 190 and the fifthbearing 165E is to allow the motor 150 to be operated in anyorientation, such as a sideways position, an upside-down position,and/or to allow the motor 150 to operate in a zero-gravity environment,for example. By way of the pressure provided to the cylinder 160 fromthe combination of the leaf spring 190 and the fifth bearing 165E, thecylinder 160 is held in place among the first through fifth bearings165A-165E. The cylinder 160 is moved by way of linear and/or rotationalforce provided by way of the motor 150 according to the firstembodiment.

As seen in FIG. 1, the first and second bearings 165A, 165B arepreferably disposed 120 degrees apart from the third and fourth bearings165C, 165D, with the fifth bearing disposed 120 degrees apart from thefirst and second bearings 165A, 165B, and disposed 120 apart from thethird and fourth bearings 165C, 165D, along an outer circumference ofthe cylinder 160. The piezo plate/bearing structures are shown fittedonto a chassis 195, with the cylinder 160 disposed within a bore 196 ofthe chassis 195 and held in place by way of the first through fifthbearings 165A-165E. Coupling units 145, each of which preferablyincludes a screw, a nut and a washer, hold the first through fourthbearings 165A-165D in place onto the chassis 195. The fifth bearing 165Eand the leaf spring 190 are also held in place within the chassis 195 bybeing snugly fit within the bore 196 with the cylinder 160 alreadydisposed within the bore 196. The fifth bearing 165E is disposed at aposition between the first through fourth bearings 165A-165D along thelongitudinal axis of the cylinder 160. Preferably, the fifth bearing165E is positioned against a mid-point (with respect to a lengthdirection) of the cylinder 160.

Motion is provided to the cylinder 160 by activating one or more of thepiezo-electric ceramic plates 180, to thereby move the bearings165A-165D that are disposed against the cylinder 160. FIG. 2A shows theshape of a shear piezo-electric ceramic plate 210 with no voltageapplied to it. When a voltage is applied to it, the piezo-electric plate210 deforms or shears, as shown in FIG. 2B. The size of the deformationor shearing, d, can be controlled by the size of the voltage applied tothe piezo-electric plate 210. By way of example and not by way oflimitation, a voltage of 200 volts applied to the top and bottomconductive plates of the piezo-electric plate 210 results in a 1.0micron deformation or shearing of the piezo-electric plate 210 (distance“d”). A lesser voltage applied to the piezo-electric plate 210 willresult in a concomitant lesser amount of deformation, as is known tothose skilled in the art.

Referring back to FIG. 1, in the first embodiment, each of the piezostacks 180 includes two piezo-electric plates 180 disposed against eachother to form a stack. In the first embodiment, the piezo plates 180 ofone piezo stack are oriented such that one piezo-electric plate deformsalong the axis of the cylinder 160, while the other piezo-electric platedeforms perpendicular to the axis of the cylinder 160.

In a second embodiment of the invention, the piezo stacks are disposedin a manner such that a first piezo plate 180 deforms along an axis 45degrees with respect to an axis of the cylinder 160, while a secondpiezo plate 180 deforms along an axis orthogonal to the axis at whichthe first piezo plate deforms. With such a disposition, when a voltageis applied across one of the piezo plates of a piezo stack, the cylinder160 is caused to move in a spiral (both linear and rotationally at thesame time) manner. When a voltage is applied across both piezo plates180 of a two-plated piezo stack at the same time, the maximum strokethat the cylinder 160 can be moved at one time is increased to 1.414(square root of two)*d, in order to get a larger stroke or movement ofthe bearing coupled to the piezo plates 180.

In either the first or second embodiments, motion of the cylinder 160 ispreferably achieved by an asymmetric voltage profile using the voltagewaveform 300 as shown in FIG. 3. The voltage waveform 300 is preferablyprovided by way of a voltage generator (not shown) being controlled by amicroprocessor, for example. Of course, other ways of providing asuitable voltage waveform may be contemplated, while remaining withinthe scope of the invention.

In the example provided below, assume that the voltage waveform shown inFIG. 3 is provided to the piezo-electric ceramic plates 180 that arecoupled to the bearings 165A, 165B, 165C, and 165D. The increase ofvoltage in a linear manner during the time period t1 is slow enough sothat as the piezo-electric ceramic plates 180 move the bearing 165Battached to it due to the shearing of the piezo-electric ceramic plates180, the static friction between the bearings 165A,B,C,D and thecylinder 160 is not broken. The static friction between the cylinder 160and the fifth bearing 165E is smaller than the static friction betweenthe cylinder 160 and the bearings 165A,B,C,D. As a result, during thetime period t1, the cylinder 160 moves with the movement of the bearings165A,B,C,D a distance “d” (see also FIG. 2B). During this time periodt1, the cylinder 160 slips on the bearing 165E. Depending on which oneof the two piezo-electric plates 180 (see also FIG. 4) is provided withthe voltage waveform 300 of FIG. 3, this movement of the cylinder 160may be either a linear movement or a rotational movement, or acombination of the two, if both plates are caused to shearsimultaneously.

Following the motion of the bearings 165A,B,C,D (and the accompanyingmovement of the cylinder 160), the voltage is rapidly dropped within atime period t2, which moves the piezo-electric ceramic plates 180holding the bearings 165A,B,C,D back to their original shape (see alsoFIG. 2A). This causes the bearings 165A,B,C,D to snap back to itsoriginal position, whereby the bearings 165A,B,C,D move back thedistance “d” with respect to the cylinder 160. Due to the sharp voltagedrop during the time period t2, acceleration of the bearings 165A,B,C,Dis large enough so as to break the static friction between the bearings165A,B,C,D and the cylinder 160. Also, the inertia of the cylinder 160is large enough such that it does not follow the quick snapping motionof the bearings 165A,B,C,D during the time period t2.

Accordingly, the bearings 165A,B,C,D slide over the outer surface of thecylinder 160 during the time period t2. This results in no movement ofthe cylinder 160 as the bearings 165A,B,C,D move quickly back to their“default” or “home” position at the end of the time period t2. Theresult is that the net motion of the cylinder 160 is approximately thedistance “d” during the combined time periods t1 and t2.

The properties of the shear piezo-electric ceramic plates 180 allow formovements of the cylinder 160 to be at an amount “d” of between 1nanometer to 1 micrometer or more. The actual amount of movement isdependent on the size and type of piezo plates used, and the amount ofdeformation that can be obtained by applying a voltage across the piezoplates.

In the first embodiment, the time period t1 must be long enough to allowthe cylinder 160 to move without the bearings 165A,B,C,D sliding alongits outer surface. If a maximum displacement of the piezo plate isdesired, the voltage ramps up from 0 volts to 200 volts during the timeperiod t1, for example. A convenient time period t1 has been determinedby the inventors to be, for example, 1 millisecond, when aluminabearings are used to move a sapphire cylinder. Also, the time period t2must be short enough to not allow the cylinder 160 to move as thebearings are snapped back to their original positions as the piezoplates 180 coupled to the bearings return to their original non-deformedshape. A convenient time period t2 has been determined by the inventorsto be, for example, 3 microseconds. Of course, one of ordinary skill inthe art will recognize that the time periods t1 and t2 depend on manyspecific details, for example on the material composition of thebearings 165A-165E and material composition of the cylinder 160 to bemoved by the bearings 165A-165E. Accordingly, other time periodlimitations for t1 and t2 may be envisioned, based on the materialcompositions of the bearings and cylinders.

The stack of two shear piezo-electric ceramic plates 180 positionedbehind each of the four active bearings 165A-165D, whereby the plates180 are oriented in perpendicular directions with respect to each other,permits both linear translation and rotation of the cylinder 160, whichallows for flexible positioning of the cylinder 160.

Two degrees of freedom of movement of a cylindrical object, one linearand the other rotational, are obtained by way of a positioning device inaccordance with the present invention. Also, by providing differentcontrol voltage waveforms to different shear-piezo plates at the sametime in the present invention, the cylinder 160 can be moved bothlinearly and rotationally at the same time, such as in a spiral manner,or in any desired manner (e.g., two degree rotation of the cylinder 160while at the same time the cylinder 160 is moved in a linear directiontwo microns towards a surface to be scanned).

In a third embodiment of the invention, the structure is the same as thefirst embodiment, except that instead of using a combination of a leafspring 190 and a slippery bearing 165E to maintain a proper amount ofpressure to hold the cylinder 160 in place among the bearings, twobearings each having respective piezo plates are used. Thus, six activebearings are disposed around the cylinder 160 in the third embodimentand are used to move the cylinder 160 either rotationally or linearly,or both. FIG. 6 shows a structure of six bi-axial piezo actuators80A-80F disposed around a cylinder 160, according to the thirdembodiment of the invention.

FIG. 5 shows a sapphire cylinder 160 by itself, which is an object to bepositioned by way of a plurality of bi-axial piezo actuators. Thecylinder 160 preferably is a hollow tube, to thereby allow a device tobe fitted (e.g., through-bolted) to the cylinder 160, whereby thatdevice can be used to stress and/or flex a sample in a desired manner.

By way of example and not by way of limitation, the range of motion ofthe cylinder 160 shown in FIG. 6 is 10 mm of linear movement and 360degrees of rotational movement, with a 1 nanometer accuracy. The forceprovided to the cylinder 160 as the cylinder 160 is held in place amongthe first through sixth actuators 80A-80F is on the order of 1-2Newtons.

FIG. 7 shows a three dimensional positioning and scanning device 810according to the fourth embodiment of the invention, whereby thebi-axial piezo actuators are not shown in that figure (but they areshown in FIG. 6) in order to more clearly show the structure of thechassis that holds the actuators in place. Three cylinders 510A, 510B,160 are provided, each of which is orthogonally positioned with respectto the other two cylinders (e.g., one cylinder 150 is situated on anx-axis, one cylinder 510A is situated on a y-axis, and one cylinder 510Bis situated on a z-axis).

In the fourth embodiment, cylinder 150 functions as an STM, whilecylinders 510A, 510B operate as stress motors for stressing and/orflexing the sample to a desired amount along the y-axis and the z-axis.Each cylinder 150, 510A, 510B is positioned within a respective bore 196of the chassis 195, and can be rotated or linearly positioned within itsrespective bore 196. Four small holes 192 are provided on the chassis860 for each bore 196, whereby a bi-axial piezo actuator (see FIG. 4) isfitted within each respective hole 192 and held in place by way of ascrew/washer/nut assembly such as assembly 145 shown in FIG. 1, forexample.

In more detail, by way of example and not by way of limitation, as eachcylinder is placed within its respective bore 196 of the chassis 195,the first through fourth actuators 80A-80D for that cylinder are screwedinto their respective holes 192 of the bore 196, and tightened in place.Then, a leaf spring, with a fifth actuator affixed thereto, is fittedwithin the bore 196, to thereby fit snugly in place within the bore 196to thereby press the cylinder against the first through fourth actuators80A-80D.

While the fourth embodiment is described with respect to five actuators,six actuators are used in a fifth embodiment, whereby the fifth andsixth actuators are ‘active’ actuators (with piezo plates used to movethose actuators), and are similar in structure to the first throughfourth actuators of the fourth embodiment. That structure is shown inFIG. 6.

The fifth and sixth actuators are preferably fitted onto a teeter-totter(not shown) and are slid into the bore 196 after the cylinder and thefirst through fourth actuators have been positioned and affixed to thechassis 195. FIG. 2B of Pan describes a suitable teeter-tooterarrangement that may be utilized in the fourth embodiment. Each cylinderis snugly fit in place within its respective bore 196 with each of thefirst through sixth actuators pressed against the outer surface of thecylinder.

The structure shown in FIG. 7 is capable of straining a sample in avariety of directions, while also being capable of scanning the sample520 while it is being strained by one or both of the strain motors 510A,510B, in order to determine the effects of the straining on the sample520.

Different embodiments of the present invention have been describedaccording to the present invention. Many modifications and variationsmay be made to the techniques and structures described and illustratedherein without departing from the spirit and scope of the invention.Accordingly, it should be understood that the apparatuses describedherein are illustrative only and are not limiting upon the scope of theinvention.

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 15. (canceled)16. A positioning apparatus for positioning an object, comprising: firstdeformation means for deforming along a first plane and along a secondplane; second deformation means for deforming along the first plane andthe second plane; third deformation means for deforming along the firstplane and the second plane; fourth deformation means for deforming alongthe first plane and the second plane; a first bearing that is fixedcoupled to the first deformation means; a second bearing that is fixedlycoupled to the second deformation means; a third bearing that is fixedlycoupled to the third deformation means; a fourth bearing that is fixedlycoupled to the fourth deformation means; pressure exerting means; and afifth bearing that is coupled to the pressure exerting means, whereinthe first through fifth bearings are disposed around and against theobject to be positioned, to provide for positioning of the object in atleast one of a linear direction and a rotational direction.
 17. Theapparatus according to claim 16, wherein the object to be positioned isa cylindrical object.
 18. The apparatus according to claim 17, whereinthe cylindrical object is a sapphire cylindrical object.
 19. Theapparatus according to claim 16, wherein the first through fourthbearings are alumina bearings.
 20. The apparatus according to claim 16,wherein the fifth bearing is a Teflon bearing.
 21. The apparatusaccording to claim 16, wherein the first deformation means comprises: afirst piezo-electric plate; and a second piezo-electric plate that isdisposed against the first piezo-electric plate.
 22. The apparatusaccording to claim 21, wherein the second deformation means comprises: athird piezo-electric plate; and a fourth piezo-electric plate that isdisposed against the third piezo-electric plate.
 23. The apparatusaccording to claim 16, wherein the first and third bearings are disposed120 degrees apart from each other with respect to an outercircumferential surface of the object.
 24. The apparatus according toclaim 16, wherein the first through fourth bearings and glued to thefirst through fourth deformation means, respectively.
 25. The apparatusaccording to claim 23, wherein the fifth bearing is disposed 120 degreesapart from the first through fourth bearings.
 26. A positioningapparatus for positioning an object, comprising: first deformation meansfor deforming along a first plane and along a second plane; seconddeformation means for deforming along the first plane and the secondplane; third deformation means for deforming along the first plane andthe second plane; fourth deformation means for deforming along the firstplane and the second plane; fifth deformation means for deforming alongthe first plane and the second plane; sixth deformation means fordeforming along the first plane and the second plane; a first bearingthat is fixed coupled to the first deformation means; a second bearingthat is fixedly coupled to the second deformation means; a third bearingthat is fixedly coupled to the third deformation means; a fourth bearingthat is fixedly coupled to the fourth deformation means; a fifth bearingthat is fixedly coupled to the fifth deformation means; and a sixthbearing that is fixedly coupled to the sixth deformation means, whereinthe first through sixth bearings are disposed around and against theobject to be positioned, to provide for positioning of the object in atleast one of a linear direction and a rotational direction.
 27. Theapparatus according to claim 26, wherein the object to be positioned isa cylindrical object.
 28. The apparatus according to claim 27, whereinthe cylindrical object is a sapphire cylindrical object.
 29. Theapparatus according to claim 26, wherein the first through sixthbearings are alumina bearings.
 30. The apparatus according to claim 26,wherein the first and second bearings are disposed on a first imaginaryplane that is tangential to an outer circumferential surface of theobject, wherein the third and fourth bearings are disposed on a secondimaginary plane that is tangential to the outer circumferential surfaceof the object, and wherein the fifth and sixth bearings are disposed ona third imaginary plane that is tangential to the outer circumferentialsurface of the object, and wherein the first, second and third planesare not co-planar.